EXCHANGE 


THE  FREE  ENERGY  OF  DILUTION  AND 

THE  ACTIVITIES  OF  THE   IONS  OF 

HYDROGEN  IODIDE  IN  AQUEOUS 

SOLUTIONS 


JUi 


A  DISSERTATION 

Submitted  to  the  Faculty  of  the  Graduate  College  of  the  State 

University  of  Iowa  in  Partial  Fulfillment  of  the 

Requirements    for    the    Degree    of 

DOCTOR  OF  PHILOSOPHY 

BY 
ARTHUR  ROY  FORTSCH 


IOWA   CITY,  IOWA 
1922 


THE  FREE  ENERGY  OF  DILUTION  AND 

THE  ACTIVITIES   OF  THE   IONS   OF 

HYDROGEN  IODIDE  IN  AQUEOUS 

SOLUTIONS 


A  DISSERTATION 

Submitted  to  the  Faculty  of  the  Graduate  College  of  the  State 

University  of  Iowa  in  Partial  Fulfillment  of  the 

Requirements    for    the    Degree    of 

DOCTOR  OF  PHILOSOPHY 

BY 

ARTHUR  ROY  FORTSCH 

i\  * 


IOWA   CITY,  IOWA 
1922 


ACKNOWLEDGEMENTS 

The  author  wishes  to  take  this  opportunity  to  express  his  ap- 
preciation for  the  kindly  assistance  and  inspiration  of  Dr.  J.  N. 
Pearce  under  whose  direction  this  research  was  carried  out. 

Thanks  are  also  extended  to. Dr.  E.  W.  Rockwood,  Dr.  L.  C. 
Raiford,  Dr.  P.  A.  Bond,  and  other  members  of  the  department 
for  their  co-operation  and  interest. 


* 
!Z 


THE   FREE    ENERGY   OF   DILUTION  AND    THE    ACTIV- 
ITIES OF  THE  IONS  OF  HYDROGEN  IODIDE 
IN  AQUEOUS  SOLUTIONS. 

Because  of  their  anomalous  behavior  solutions  of  strong  elec- 
trolytes have  long  occupied  the  attention  of  numerous  investigat- 
ors. Many  attempts  have  been  made  to  provide  a  theoretical 
explanation  of  the  abnormalities.  Of  the  various  solution  prop- 
erties the  free  energies  of  dilution  and  the  activities  of  the  ions 
have  been  especially  studied.  From  calculations  based  on  the 
assumption  that  a  common  ion  at  any  given  concentration  has 
the  same  mobility  regardless  of  the  associated  ion  G.  N.  Lewis1 
concluded  that  the  chlorides,  bromides,  and  iodides  of  hydrogen 
and  of  the  alkali  halides  are  equally  dissociated  in  tenth  molal 
solutions.  In  order  to  explain  changes  in  transport  numbers  he 
advances  two  hypotheses:  (1)  "that  all  the  ions  increase  in 
mobility  with  increasing  ion-concentration,  the  increase  being 
relatively  greater,  the  greater  the  original  mobility;  (2)  that  all 
the  ions  decrease  in  mobility  with  increasing  ion-concentration, 
the  decrease  being  greater  the  smaller  the  original  mobility. "  He 
favors  the  first  of  these  and  advances  as  probable  causes:  (1)  a 
gradual  dehydration  which  although  undoubtedly  present,  does 
not  play  a  dominant  part,  and  (2)  an  added  increase  in  the 
ordinary  conductivity  of  the  electrolyte  due  to  a  conduction  of 
the  Grotthus  type. 

Maclnnes2  using  the  same  assumption  has  found  that  the 
alkali  chlorides  are  equally  dissociated  in  hundredth  molal  solu- 
tions. His  observations  led  him  to  assume  that  the  activity  of 
the  chloride  ion  is  independent  of  the  cation  associated  with  it. 
The  similarity  of  the  potassium  ion  and  the  chloride  ion  with 
respect  to  atomic  weight,  atomic  volume,  ionic  mobility,  and 
other  properties,  led  him  to  assume  that  their  activities  are  also 
equal  in  solutions  of  potassium  chloride. 

Of  the  various  investigations  only  those  most  closely  connected 


i  J.  Am.  Chem.   Soc.,  34,   1631    (1912). 
-  J.   Am.   Chem.   Soc.,  41,   1086    (1919). 

3 


4  A  DISSERTATION 

with  this  research  will  be  mentioned  here.  Noyes  and  Maclnnes3 
have  computed  the  mean  activity  coefficients  of  the  ions  of  potas- 
sium chloride,  hydrogen  chloride,  lithium  chloride,  and  potassium 
hydroxide.  Harned4'5  on  the  basis  of  theoretical  considerations 
has  developed  a  semi-empirical  relation  between  the  activity 
coefficient  of  an  electrolyte  and  the  molal  concentration  and  has 
calculated  the  activities  of  the  various  ions  from  the  experimental 
data  of  himself  and  others.  He  concludes  that  the  assumptions 
of  Noyes  and  Maclnnes6  are  true  within  certain  limits  and  that 
the  theory  of  complete  ionization  of  strong  electrolytes  is  a  good 
working  hypothesis.  His  work  gives  us  a  very  valuable  sum- 
mary of  preceding  investigations.  In  connection  with  this  theory 
of  complete  dissociation  of  strong  electrolytes,  we  may  note  that 
it  wras  first  suggested  by  Noyes7  and  was  further  developed  and 
substantiated  by  Milner8,  Ghosh9,  Bjerrum10,  Bronsted11,  Hill12, 
and  others.  Finally  we  have  the  very  complete  work  of  Lewis 
and  Randall13.  They  discuss  the  four  methods  of  experimentally 
determining  activity  coefficients,  namely:  activity  from  vapor 
pressure  of  the  solvent;  activity  from  vapor  pressure  of  the 
solute ;  activities  from  electromotive  force ;  and  activity  coefficients 
from  freezing  point  data.  They  also  give  the  numerical  values 
of  the  activities  of  the  various  ions  at  different  concentrations, 
determined  by  one  or  more  of  the  above  methods. 

A  very  important  relation  in  regard  to  ionic  activity  was 
pointed  out  by  Lewis  and  Randall14  and  at  about  the  same  time 
by  Pearce  and  Hart15.  Lewis  and  Randall,  using  the  experi- 
mental data  of  Bates  and  Kirschmann16  on  partial  vapor  pres- 
sures of  the  hydrogen  halides,  showed  that  the  activities  of  the 


s  J.  Am.  Chem.  Soc.,  42,  239  (1920). 
*  J.  Am.  Chem.  Soc.,  42,  1808  (1920). 
s  J.  Am.  Chem.  Soc.,  44,  252  (1922). 

6  loc.    cit. 

7  Congress.     Arts  &  Sciences,  St.  Louis  Exposition,  4,   389    (1904). 

s  Phil.  Mag.,    (6)    23,  551    (1912);    25,   753    (1913);   35,   352    (1918). 

»  J.  Am.  Chem.  Soc.,  113,  449    (1918);    113,  627    (1918);   113,   707    (1918). 

10  Z.  Electro  Chem.,  24,   321    (1918)  ;    Z.  Anorg.  Chem.,   109,  275    (1920) 

11  J.  Am.  Chem.  Soc.,  42,   761    (1920). 

12  Ibid.,  43,  254    (1920). 

is  J.  Am.  Chem.   Soc.,   43,    1152    (1921). 
i*  loc.   cit. 

is  J.   Am.  Chem.   Soc.,  43,   2483    (1921). 
16  J.  Am.  Chem.  Soc.,  41,  1991    (1919). 


A  STUDY  OF  THE  IONS  OF  HYDROGEN  IODIDE        5 

chloride,  bromide,  and  iodide  ions  are  equal  at  equal  concen- 
trations. Pearce  and  Hart,  using  the  electromotive  force  method, 
showed  that  the  chloride  and  bromide  ion  activities  are  equal 
at  equal  concentrations.  It  was  considered  expedient  in  view 
of  these  facts  to  add  to  the  investigations  by  making  a  study 
of  the  free  energy  of  dilution  and  the  activities  of  the  ions  in 
aqueous  solutions  of  hydrogen  iodide. 


FIGURE  1 

Apparatus  and  Materials. 

The  method  used  in  this  research  is  similar  to  that  of  Linhart17,. 
the  iodide  being  substituted  for  the  chloride.  The  silver  iodide 
was  made  by  precipitation  from  a  solution  of  potassium  iodide 
by  means  of  silver  nitrate  solution.  The  potassium  iodide  was 
purified  by  crystallizing  twice  from  conductivity  water.  The 
silver  nitrate  was  the  "Baker's  Analysed"  product.  The  precip- 


17  J.   Am.   Chem.    Soc.,   41,   1175    (1919). 


6 


A  DISSERTATION 


itate  was  washed  first  with  distilled  water  until  the  washings 
gave  no  test  for  iodides,  and  then  washed  several  times  with 
conductivity  water.  The  whole  operation  was  carried  out  at 
night.  It  was  finally  stored  under  conductivity  water,  care  being 


FIGURE  2 


used  to  exclude  all  light  from  the  product.  By  using  these 
precautions  the  silver  iodide  could  be  preserved  indefinitely  with 
no  apparent  darkening. 

The  metallic  silver  was  obtained  by  electrolysis  of  silver  nitrate 
solution,  using  a  platinum  wire  anode  and  a  current  of  4  to  5 
amperes.  This  gave  a  finely  divided  crystalline  mass  of  metallic 
silver.  The  silver  after  being  carefully  washed  was  stored  under 
conductivity  water  until  needed. 


A  STUDY  OF  THE  IONS  OP  HYDROGEN  IODIDE        7 

The  hydrogen  iodide  was  made  by  passing  hydrogen  sulphide 
gas  into  an  aqueous  suspension  of  resublimed  iodine.  The  prod- 
uct was  distilled  and  the  fraction  of  constant  boiling  point  sep- 
arated. This  was  kept  in  a  flask  over  a  trace  of  red  phosphorus 
and  was  freshly  distilled  in  a  current  of  hydrogen  gas  when 
needed. 

In  making  up  the  solutions,  approximately  the  required  amount 
of  hydrogen  iodide  was  added  to  conductivity  water  which  had 
been  previously  boiled,  and  about  a  liter  of  solution  made  up. 
The  cell  which  held  approximately  550  c.c.  was  thoroughly 
cleaned,  rinsed  several  times  with  the  solution,  filled  to  the 
proper  volume,  and  finally  placed  in  a  large  oil-bath  to  come  to 
equilibrium.  The  time  required  was  from  four  to  eight  days, 
depending  somewhat  upon  the  concentration.  The  bath  heater 
was  controlled  to  give  any  temperature  desired  within  ±0.03°. 
The  exact  concentration  of  the  hydrogen  iodide  used  in  each  cell 
was  determined  at  the  end  of  each  set-up,  the  iodine  content 
being  accurately  determined  in  duplicate  by  precipitation  with 
silver  nitrate  solution. 

The  hydrogen  electrodes  were  prepared  by  the  method  of 
Lewis,  Brighton,  and  Sebastian18.  Two  platinum  gauze  electrodes 
were  electrolysed  in  a  one  per  cent  solution  of  platinum  chloride 
with  a  current  of  about  0.05  ampere.  The  direction  of  the 
current  was  alternated  every  five  minutes  for  two  hours.  The 
preparation  of  the  electrodes  was  completed  by  electrolysing  first 
in  a  dilute  solution  of  potassium  hydroxide  and  then  in  dilute 
sulphuric  acid  solution.  They  were  thoroughly  washed  in  con- 
ductivity water  and  allowed  to  stand  in  conductivity  water  for 
several  hours,  after  which  time  they  were  placed  in  the  cell. 

The  hydrogen  was  obtained  by  electrolysis  of  sodium  hydroxide 
solution.  The  gas  was  passed  through  a  solution  of  potassium 
pyrogallate,  then  through  concentrated  sulphuric  acid,  and  on 
through  the  saturator  into  the  cell.  The  saturator  was  merely 
a  series  of  bulbs  through  which  the  hydrogen  passed  before  enter- 
ing the  cell.  This  saturator  contained  a  solution  of  the  same 
strength  as  that  in  the  cell  and  thus  any  change  in  concentration 
due  to  unsaturated  hydrogen  gas  was  avoided.  The  flow  of  the 

is  J.  Am.  Chem.  Soc.,   39,  2245    (1917). 


8  A  DISSERTATION 

hydrogen  through  the  cell  was  regulated  by  means  of  a  stop  cock 
to  about  sixty  bubbles  per  minute.  The  cell  and  saturator  are 
shown  in  Fig.  1,  while  Pig.  2  shows  the  generator  and  the  stor- 
age bottle  through  which  the  hydrogen  passed  before  entering 
the  cell. 

The  measurement  of  the  potentials  was  made  on  a  Wolff  po- 
tentiometer, the  reference  standard  being  a  certified  cadmium- 
Weston  cell.  (No.  4554;  1.01871  volts  at  23°). 

Accuracy  of  Method. 

Electromotive  force  readings  were  taken  on  the  two  electrodes 
independently  and  unless  the  variation  between  the  two  was  less 
than  0.04  m.  v.  the  process  of  preparation  was  repeated.  Cases 
where  a  repetition  was  necessary  were  very  rare.  All  electro- 
motive force  readings  were  corrected  by  applying  the  formula: 

.00019837  T  760 

E   =  Iog10    

2  x 

where  E  is  the  correction,  T  the  absolute  temperature,  and  x  is 
the  pressure  of  the  hydrogen.  The  value  of  x  was  determined 
by  a  standard  barometer  the  readings  being  corrected  for  lati- 
tude, altitude,  and  temperature. 

Preliminary  experiments  were  made  to  determine  the  effect 
of  the  rate  of  bubbling.  It  was  found  that  the  rate  could  be 
varied  from  30  to  250  per  minute  without  affecting  the  constancy 
of  the  readings. 

The  temperatures  of  the  experiment  were  25°,  30°,  and  35°. 
They  were  taken  in  the  order  named  and  then  to  ascertain 
whether  any  changes  had  occurred  during  the  experiment  the 
temperature  was  lowered  to  25°  and  readings  were  again  taken. 
The  time  required  to  complete  this  series  was  ten  days.  In  the 
preliminary  work  it  was  found  that  there  is  a  variation  which 
becomes  apparent  when  the  electrodes  are  left  in  the  solution 
over  sixty  hours.  But  by  removing  the  electrodes,  allowing  them 
to  stand  in  concentrated  nitric  acid  for  an  hour  or  more,  and 
replatinizing  this  effect  was  reduced  to  0.10  m.  v.  or  less  in 
solutions  whose  concentration  was  below  0.02  M.  per  1000  grams 
of  water.  In  the  more  concentrated  solutions,  however,  it  was 


A  STUDY  OF  THE  IONS  OF  HYDROGEN  IODIDE        9 

apparently  impossible  to  eliminate  the  variation,  but  at  any  one 
temperature  the  electromotive  forces  became  constant  showing 
that  equilibrium  had  been  reached.  When  four  consecutive  read- 
ings taken  two  hours  apart  which  differed  among  themselves  by 
less  than  0.04  m.  v.  were  secured,  this  was  considered  as  evidence 
that  equilibrium  had  been  attained.  The  greatest  variation  of 
the  electromotive  force  readings  between  the  initial  25°  set  and 
the  final  25°  set  was  recorded  at  the  highest  concentration.  In 
this  case  it  was  0.85  m.v.  Furthermore,  at  concentration  0.12972  M 
a  slight  turbidity  was  obtained  by  adding  a  chloride  to  the 
solution  secured  by  allowing  the  electrodes  to  stand  in  concen- 
trated nitric  acid,  but  there  was  not  a  weighable  amount  of 
silver  chloride.  At  concentration  of  0.24608  M.  the  amount  of 
silver  was  larger  but  did  not  exceed  a  few  milligrams.  At  higher 
concentrations  than  this  the  amount  of  silver  deposited  on  the 
platinum  electrodes  became  considerable  and  no  consistent  read- 
ings could  be  obtained. 

Measurement  of  tine  Cells. 

Table  I   gives  the  final  values  of  the  electromotive   force  of 
the  cells  at  various  concentrations  and  at  25°,  30°,  and  35°. 

TABLE  I. 

Electromotive  Force  of  the  Cells: 
H. 


c. 

E25. 

\V7  1     ••"••o          1 

E30. 

Ess- 

1000  g. 

volts. 

volts. 

volts. 

0.24608 

—0.06905 

—0.06864 

—0.06829 

0.12972 

—0.03615 

—0.03556 

—0.03531 

(0.10000) 

—  (0.02273) 

—  (0.02202) 

-(0.02162) 

0.07914 

—0.01210 

—0.01128 

—0.01073 

0.05049 

+0.01006 

+0.01128 

+0.01235 

0.01981 

+0.05735 

+0.05931 

+0.06083 

0.01045 

+0.08825 

+0.09060 

+0.09262 

0.00505 

+0.12417 

+0.12707 

+0.12964 

(0.00500) 

+  (0.12453) 

+  (0.12744) 

+  (0.13001) 

The  values  of  E    (in  parenthesis)   for  the  concentration  0.005 
were  obtained  by  assuming  E  as  an  empirical  quadratic  function 


10  A  DISSERTATION 

of  (c)  using  the  three  concentrations,  0.01981,  0.01045,  and 
0.00505.  Those  for  0.100  were  obtained  in  a  similar  manner 
using  concentrations,  0.24608,  0.12972,  and  0.07914.  It  will  be 
noted  that  a  change  of  sign  occurs  between  the  concentrations 
0.07914  and  0.05049.  This  is  due  to  the  fact  that  silver  iodide 
is  extremely  insoluble;  a  small  concentration  of  hydrogen  iodide 
is  sufficient  by  the  common  ion  effect  to  reduce  the  concentration 
of  the  silver  ion  to  such  an  extent  that  the  potential  of  Ag  |  Agl, 
HI  is  less  than  the  potential  H2  |  HI.  So  far  as  the  author 
has  been  able  to  ascertain  this  circumstance  is  unique  in  inves- 
tigations of  free  energies  and  activities  of  ions. 

Free  Energy  Change  Attending  the  Cell  Reaction. 

Table  II  gives  the  free  energy  change  accompanying  the  cell 
reaction.  The  free  energy  decrease  ( — AF)  in  joules  is  obtained 
by  multiplying  the  corresponding  value  of  the  electromotive 
force  in  volts  by  96494.  The  data  are  self-explanatory. 

TABLE  II. 
Free  Energy  Change  Attending  the  Cell  Reaction. 

c.  (— AF)25.  (— AF)30.  (— AF)35. 

1000  g.  joules.  joules.  joules. 

0.24608  —6662.9  —6623.3  —6589.6 

0.12972  —3488.3  —3431.3  —3407.2 

(.0.10000)  —(2193.3)  _(2124.8)  —(2086.2) 

0.07914  —1167.6  —1088.5  —1035.4 

0.05049  +970.3  +1088.5  +1191.7 

0.01981  +5533.9  +5723.1  +5869.7 

0.01045  +8515.6  +8742.4  +8937.3 

0.00505  +11981.7  +12261.5  +12509.5 

(0.00500)  -M12016.4)  +(12297.2)  +(12545.2) 

Temperature   Coefficients   of  Free  Energy  Decrease,   and  Heat- 
Content   Decrease  Accompanying   the   Cell   Reaction. 

In  Table  III  are  given  the  values  of  a  and  (3  for  the  various 
concentrations,  calculated  from  the  relation: 

(—  AF)       —     (— AF)        (  l+ct(t— 25)+  (3   (t— 25)2). 


A  STUDY  OF  THE  IONS  OF  HYDROGEN  IODIDE      11 

The  values  of  the  decrease  in  heat-content  ( — AH)25  are  given 
in  column  four  of  the  table,  being  computed  from  the  formula: 

(— AH)25  =  (_ AF)25     (1— 298.09a). 

Upon  substituting  the  expression  for  ( — AF)  as  a  temperature 
function  for  any  given  concentration  in  the  fundamental  thermo- 
dynamic  equation: 

d          ( _AF )  4-AH 


dT  T  T2 

performing   the    differentiation    indicated,    and   rearranging   the 
terms  the  above  relation  for   ( — AH)25  is  obtained 

TABLE  III. 
Values   of   Temperature   Coefficients   and   Heat-Content 

Decrease  at  the  Various  Concentrations. 

c.  «  P  (~AH)25. 

1000  g.  X  10*  X  10T  joules. 

0.24608  -1277.1  +177.1  —9199.5 

0.12972  -4211.3  +1886.3  —7867.2 

(0.10000)  _(7609.5)  +(2726.5)  —(7168.1) 

0.07914  —16151.6  +4453.6  —6789.1 

0.05049  +25909.5  —3091.8  —6523.8 

0.01981  +7607.7  -1539.6  —7015.9 

0.01045  +5699.7  —747.8  —5952.6 

0.00505  +4950.4  —530.9  —5699.2 

(0.00500)  +(4950.1)  -(549.4)  -(5715.0) 

It  will  be  noted  that  the  values  a  and  (3  change  sign  between 
the  concentrations  0.05049  M.  and  0.07914  M.  Ellis19  likewise 
notes  a  change  of  sign  of  «  for  hydrochloric  acid  between  the 
concentrations  0.33757  M.  and  0.10040  M.  In  his  case,  however, 
the  change  is  due  to  a  distinct  change  in  the  temperature  effect, 
whereas,  in  the  case  of  hydriodic  acid  in  every  instance  the  free 
energy  of  the  cell  reaction  is  greater  the  higher  the  temperature, 
the  change  being  caused  by  a  change  in  the  sign  of  the  electro- 
motive force  of  the  cell.  At  some  concentration  intermediate 
to  0.05049  M.  and  0.07914  M.  the  electromotive  force  and  hence 
the  free  energy  decrease  is  zero.  Thus  the  values  of  «  must 


19  J.  Am.   Chem.  Soc.,   38,   737    (1916). 


12  A  DISSERTATION 

change  from  a  small  negative  number  to  an  infinitely  large 
negative  number  on  the  one  hand,  and  from  an  infinitely  large 
positive  number  to  a  small  positive  number  on  the  other  hand. 
Except  for  the  one  value— 7015.9  at  concentration  0.01981  M. 
the  values  of  — AH  show  an  increase  with  decreasing  concentra- 
tion similar  to  those  found  by  Ellis20  for  hydrochloric  acid.  The 
values  for  hydriodic  acid  are,  however,  much  smaller  and  are 
negative  instead  of  positive. 

Free  Energy  Decrease  Accompanying  the  Transfer  of  One  Mole 
of  Hydrogen  Iodide  From  the   Various  Concen- 
trations   (c)    to   0.100   M. 

From  the  free  energy  decrease  attending  the  cell  reaction  at 
the  various  concentrations  we  can  obtain,  by  taking  the  algebraic 
sum,  the  free  energy  decrease  attending  the  transfer  of  one  mole 
of  hydrogen  iodide  from  a  solution  of  any  given  concentration 
to  one  exactly  0.100  M.  These  values  are  given  in  Table  IV. 

TABLE  IV. 

Free  Energy  Decrease  Attending  the  Transfer  of  One  Mole 
of  Hydrogen  Iodide  from  Concentration  (c)  to  0.100  M. 

c.  ( — AF)25.  ( — AF)30.  ( — AF)35. 

1000  g.  joules.  joules.  joules. 

0.24608  +4469.6  +4498.5  +4503.4 

0.12972  +1295.0  +1306.5  +1321.0 

0.07914  —1025.7  —1036.3  —1086.2 

0.05049  —3163.6  —3213.3  —3277.9 

0.01981  —7727.2  —7847.9  —7955.9 

0.01045  -10708.9  —10867.2  —11023.5 

0.00505  —14175.0  -14386.3  —14595.7 

(0.00500)  -(14209.7)  -(14422.0)  -(14631.4) 

For  the  sake  of  comparison  let  us  consider  the  transfer  of  one 

mole   from   0.01045    M.   to   0.100    M.,    and    from    0.00500   M.    to 

0.05049  M.    In  the  first  case  the  value  of  —  AF25  is  10709.  joules, 

in  the  second  case  —A  F25   is  11146  joules.     For  hydrochloric 

acid  Noyes  and  Ellis21  found  for  the  transfer  from  0.00948  to 

20  loc.  cit. 

21  J.  Am.  Chem.  Soc.,  39,  2532    (1917). 


A  STUDY  OF  THE  IONS  OF  HYDROGEN  IODIDE      13 

0.100  M.—  AF25  to  be  11044.  joules,  and  from  0.003378  M.  to 
0.03324  M.,  10924  joules.  As  these  changes  are  approximately 
tenfold  they  may  be  compared  with  the  theoretical  value  11418. 
joules.  (—  AF  =  2.303  N  R  T).  It  will  be  seen  that  during 
the  range  of  concentration  0.00500  to  0.05049  M.,  hydrogen  iodide 
functions  more  nearly  as  a  perfect  solute  than  hydrogen  chloride. 
As  we  shall  see  later,  this  is  also  shown  by  the  values  of  the 
activity  coefficients. 

The   Calculation  of  Activity   Coefficients. 

The  values  of  the  electromotive  force  at  concentration 
0.00500  M.  were  found  by  assuming  that  E  is  a  quadratic  func- 
tion of  (c)  using  the  values  0.00505,  0.01045,  and  0.01981  for 
the  concentrations  and  the  corresponding  values  of  the  electro- 
motive forces  at  25°C.  The  cell  combination  was  of  the  type: 
H2|HI(c=X)05....HI(c=.005),  Agl  AgAg  |  Agl,  HI(c)....HI(c)|H2. 
The  product  of  the  activity  coefficients  of  the  ions  has  been  com- 
puted according  to  the  usual  formula: 


log  -  =  RT  log 


a2+.a,—  (c2)2a2-J-.a2— 

where   a^  a2,   refer  to  activity   coefficient   products,   and 

ttj,    cc2,   refer   to   activity   coefficients,   the    other   symbols 

having  their  usual  significance.  These  computations  have  been 
made  on  the  assumption  that  for  0.005  M.  hydrogen  iodide 
a-}-. a —  has  the  same  value  as  for  0.005  M.  hydrogen  chloride. 
According  to  Noyes  and  Maclnnes22  this  value  is  (965)2  or 
.9312.  while  according  to  Lewis  and  Randall3  it  is  (.947)2  or 
.8968.  Column  three  of  Table  V  gives  the  Values  of  a-f-.a — 

H          I 

using  .9312  as  a  basis,  while  column  four  gives  the  activity 
coefficient  products  using  .8968  as  a  basis.  These  values  were 
plotted  against  the  concentrations  on  large  scale  and  the  values 
of  a-j-.o —  corresponding  to  round  concentrations  were  read 

H          I 

off.  The  square  roots  of  these  values  give  us  the  activity 
coefficients.  These  are  given  in  Table  VI  while  similar  values 

22  ioc.  cit. 

23    Ioc.     Cit. 


14  A  DISSERTATION 

for  hydrochloric  acid  are  given  in  adjoining  columns  for  com- 
parison. 

TABLE  V. 
Activity  Coefficient  Products. 

c  AE.  a+.a—  a+.a— 

HI  HI 

1000  g.  volts. 

0.00500  0.00000  .9312  .8968 

0.01045  0.03628  .8748  .8331 

0.01981  0.06718  .8111  .7724 

0.05049  0.11447  .7866  .7491 

0.07914  0.13663  .7585  .7223 

0.12972  0.16068  .7200  .6856 

0.24608  0.19358  .7201  .6857 

TABLE  VI. 


Activity  Coefficients   Va+-« —  at  Round  Concentrations, 
c.  HI.  HCI.  HI.  HCI. 

1000  g.  (exp.)  (N-M)  (exp.)  (L-R) 

0.005  .965  .965  .947  .947 

0.010  .937  .932  .920  .924 

0.020  .901  (.899)  .886  .894 

0.030  .893  .880  .877 

0.050  .884  .855  .868  .860 

0.100  .862  .823  .846  .814 

0.200  .849  .796  .834  .783 

On  the  assumption  that  the  activity  of  the  ions  is  independ- 
ent, and  that  the  activities  of  the  chloride,  bromide,  and  iodide 
ions  are  equal,  we  should  expect  the  same  activity  coefficients 
for  hydrogen  iodide  as  were  found  for  hydrogen  chloride. 
Whether  we  use  the  value  .965  or  .947  for  the  activity  coeffic- 
ient of  0.005  M.  hydrogen  iodide,  a  glance  at  Table  VI  shows 
that  the  coefficients  are  not  equal  throughout  the  whole  range 
of  concentrations  investigated.  The  agreement  with  similar 
magnitudes  for  hydrochloric  acid  by  Noyes  and  Maclnnes24 
is  good  where  the  concentrations  are  less  than  0.030  M.,  but 
the  agreement  with  Lewis  and  Randall25  is  better  for  a  greater 


24  IOC.    Cit. 

25  loc.  cit. 


A  STUDY  OF  THE  IONS  OF  HYDROGEN  IODIDE      15 

range  namely,  for  concentrations  from  0.005  M.  to  0.050  M. 
From  the  data  on  the  activity  coefficients  of  hydrochloric  acid 
it  may  be  noted  that  there  is  a  minimum  of  activity  between 
0.50  M.  and  1.00  M.  From  this  investigation  we  are  led  to 
the  conclusion  that  the  same  type  of  variation  is  exhibited  by 
the  activity  coefficients  of  hydrogen  iodide,  but  that  the  mini- 
mum occurs  at  a  lower  concentration,  0.20  M.  For  the  con- 
centrations from  0.005  M.  to  0.050  M.  the  assumption,  that  the 
activities  of  the  halide  ions  are  equal  appears  to  be  valid. 
Beyond  that  concentration  the  evidence  is  against  the  validity 
of  the  assumption.  It  would  be  desirable  to  have  additional 
information  from  a  similar  study  of  hydrogen  bromide  solutions 
before  passing  a  final  opinion. 

In  regard  to  the  slightly  different  values  of  activity  coeffic- 
ients from  different  sources,  it  is  apparent  that  the  difference 
lies  mainly  in  the  standard  of  reference  chosen.  Noyes  and 
Maclnnes  26  have  arbitrarily  $et  the  activity  coefficient  at  the 
lowest  concentration  at  which  the  electromotive  forces  are  de- 
pendable equal  to  the  conductance  viscosity  ratio.  In  the  case 
of  hydrochloric  acid  the  activity  coefficient  of  0.003324M.  solu- 
tion has  been  taken  as  .985.  Lewis  and  Randall27  have  used 
as  a  basis  of  their  values  for  hydrochloric  acid  a  method  of 
extrapolation  described  by  Linhart.28  Any  error  in  either 
standard  would  influence  the  entire  series  of  activity  coefficients. 
Pearce  and  Hart29  working  with  solutions  of  potassium  bromide, 
and  using  a  method  similar  to  Noyes  and  Maclnnes  obtained 
activity  coefficient  products  which  agree  with  the  results  of 
those  investigators  in  their  work  on  potassium  chloride  solu- 
tions. In  this  research,  using  the  method  of  Linhart30,  data 
have  been  obtained  for  hydrogen  iodide  which  agree  with  his 
values  of  the  activity  coefficients  of  hydrogen  chloride  for  a 
considerable  range  in  the  dilute  solutions.  Thus  with  the 
meager  information  at  hand  we  are  not  justified  in  definitely 
stating  which  standard  is  correct. 

26  loc.  cit. 

27  loc.  eit. 

28  loc.    Cit. 

29  loc.  cit. 
so  loc.  cit. 


16  A  DISSERTATION 

SUMMARY 

1.  Measurement  of  the  electromotive  force   of  the  cells: 

H2   |  HI    (c).... HI    (c),  Agl       Ag, 

at   various  concentrations  have  been   made. 

2.  The  free  energy  decrease  of  the  cell  reaction,  and  the  heat- 
content  decrease  of  the  cell  reaction  have  been  computed. 

3.  The  free  energy  decrease  accompanying  the  transfer  of  one 

mole   of   hydrogen   iodide   from    the    various    concentrations 
to  0.10  molal  have  been  calculated. 

4.  From    the    values    of    the    electromotive    force    of    the    com- 
bination : 

H2!HI(.005)....HI(.005),  Agl  |  AgAg  |  Agl,  HI(c)....HI(c)|H2 
the  activity  coefficients  have  been  calculated  by  the  usual 
formula.  From  these  values  the  activity  coefficients  at 
round  concentrations  have  been  determined.  From  the  data 
obtained  it  has  been  concluded  that  the  activities  of  the 
chloride  and  iodide  ions  are  equal  up  to  a  concentration  0.05 
molal  but  beyond  that  concentration  the  assumption  does 
not  appear  to  hold. 


BIOGRAPHY 

Arthur  Roy  Fortsch  received  his  early  education  in  the  rural 
schools  of  Fayette  County  and  Bremer  County,  Iowa.  After 
two  years  of  teaching  in  the  rural  schools,  he  entered  Iowa 
State  Teachers  College,  Cedar  Falls,  Iowa  in  1911,  receiving  his 
A.  B.  degree  in  1915.  In  1915  he  entered  the  University  of 
Iowa.  He  received  the  degree  of  Master  of  Science  in  1916. 
With  the  exception  of  thirteen  months  in  the  Army  and  a 
year  teaching  physics  and  chemistry  in  Mason  City  Junior 
College,  Mason  City,  Iowa,  he  has  continued  in  graduate  work 
at  the  University  since  that  time.  He  is  a  member  of  the 
American  Chemical  Society,  Sigma  Xi,  Delta  Sigma  Rho,  and 
and  Gamma  Alpha  graduate  scientific  fraternity.  At  present 
he  is  employed  as  research  chemist  by  the  Standard  Oil  Com- 
pany, Whiting,  Indiana. 


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